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Recueil de travaux offerts par les auteurs à H. A. Lorentz à l'occassion du 25me anniversaire de son doctorat le 11 décembre 1900

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In (35), (38), (87)

•ri,*

r~J o

re presents tlie meau temparature (above tlie staiulard) of tlie solui cyliniler of radius r. It is to be remarked tliat tlie doublé refraction of tlie ray at r is independent of tlie values of 4 bevond r, and also of any boundarv-pressure. If 4 increases (or decreases) continuously froui tlie centre outxvards, tlie doublé refraction liever vaiiishes, and no dark cir-

cle is seen in tlie polariscope.

In the above solution if tlie eylinder is terininated by «at faces. we must imagine suitable forces /.', given by (2b), to be operative over the faces. The iutegral of these forces may be reduced to zero by allowing a suitable expansion parallel to the axis. llegarding dirih as a constant inot necessarily zero), independent ot r and z, we have in place ot ' »^)

*-*@ + 0 + O+*»Z-" (:IS)

The additions to P and Q are /. du-tl:, wliile (P—U) remains unclianged.

If the eylinder is long relatively to its diameter, tlie last state ot tliings mav be supposed to remain approximately unclianged, i\t n tliough the terminal faces be free froni applied force. In the neighbourhood of the ends there will be local disturbances, requiring a more elaborate analysis for tlieir calculation, hut the simple solution will applv to the greater part of the lengtli.

The case of a tliin plate wliose faces are everywliere free froni applied force is more ditticult to tieat in a rigorous manner, hut the tollowing is probably a sufficiënt account of the matter. By supposing /J=0 m (:5 b) we get

o+M£-H-*(£+?)< <*>

and using this value of dtr </:,

» ^ ('<": . ^"<1 (io)

,lr^r) '<lr >.+2y

Q= (''" + "^+2/"- (41)

/, ■-)- iy.\dr 1 rJ r >.-\-~y.